from builtins import range
import numpy as np
from random import shuffle
from past.builtins import xrange

def softmax_loss_naive(W, X, y, reg):
    """
    Softmax loss function, naive implementation (with loops)

    Inputs have dimension D, there are C classes, and we operate on minibatches
    of N examples.

    Inputs:
    - W: A numpy array of shape (D, C) containing weights.
    - X: A numpy array of shape (N, D) containing a minibatch of data.
    - y: A numpy array of shape (N,) containing training labels; y[i] = c means
      that X[i] has label c, where 0 <= c < C.
    - reg: (float) regularization strength

    Returns a tuple of:
    - loss as single float
    - gradient with respect to weights W; an array of same shape as W
    """
    # Initialize the loss and gradient to zero.
    loss = 0.0
    dW = np.zeros_like(W)

    #############################################################################
    # TODO: Compute the softmax loss and its gradient using explicit loops.     #
    # Store the loss in loss and the gradient in dW. If you are not careful     #
    # here, it is easy to run into numeric instability. Don't forget the        #
    # regularization!                                                           #
    #############################################################################
    N,C=X.shape[0],W.shape[1]
    for i in range(N):
      f =X[i].dot(W)
      f -= np.max(f)
      p=np.exp(f[y[i]])/np.sum(np.exp(f))
      loss += -np.log(p)
      dW[:,y[i]]-=X[i]
      s=np.sum(np.exp(f))
      for j in range(C):
        dW[:,j]+=np.exp(f[j])/s *X[i]
    loss =loss/N+0.5*reg*np.sum(W*W)
    dW =dW/N+reg*W

    return loss, dW


def softmax_loss_vectorized(W, X, y, reg):
    """
    Softmax loss function, vectorized version.

    Inputs and outputs are the same as softmax_loss_naive.
    
    Inputs:
    - W: A numpy array of shape (D, C) containing weights.
    - X: A numpy array of shape (N, D) containing a minibatch of data.
    - y: A numpy array of shape (N,) containing training labels; y[i] = c means
      that X[i] has label c, where 0 <= c < C.
    - reg: (float) regularization strength
    """
    # Initialize the loss and gradient to zero.
    loss = 0.0
    dW = np.zeros_like(W)

    #############################################################################
    # TODO: Compute the softmax loss and its gradient using no explicit loops.  #
    # Store the loss in loss and the gradient in dW. If you are not careful     #
    # here, it is easy to run into numeric instability. Don't forget the        #
    # regularization!                                                           #
    #############################################################################
    N=X.shape[0]
    f =np.dot(X,W)
    f -=np.max(f,axis=1).reshape(N,1)
    s = np.exp(f).sum(axis = 1)
    loss=(-np.sum(f[range(N),y])+np.sum(np.log(s)))/N+0.5*reg*np.sum(W*W)
    count =np.exp(f)/s.reshape(N,1)
    count[range(N),y] -=1
    dW =np.dot(X.T,count)/N+reg*W

    return loss, dW
